Question

Find the critical point of the function f(x,y)=-6-7x+x^2+8y-7y^2

This critical point is a ?

Answer #1

Consider the function f(x,y) = -8x^2-8y^2+x+y
Select all that apply:
1. The function has two critical points
2. The function has a saddle point
3. The function has a local maximum
4. The function has a local minimum
5. The function has one critical point
*Please show your work so I can follow along*

Find the Critical point(s) of the function f(x, y) = x^2 + y^2 +
xy - 3x - 5. Then determine whether each critical point is a local
maximum, local minimum, or saddle point. Then find the value of the
function at the extreme(s).

Use Lagrange Multiplers to find the minimum of the function
subject to the given constraint(s).
f(x,y,z,t)=7x+7y+7z+7t,
7(x2+y2+z2+t2)=8

Consider the vector field →F=〈3x+7y,7x+5y〉F→=〈3x+7y,7x+5y〉
Is this vector field Conservative? yes or no
If so:
Find a function ff so that →F=∇fF→=∇f
f(x,y) =_____ + K
Use your answer to evaluate ∫C→F⋅d→r∫CF→⋅dr→ along the curve C:
→r(t)=t2→i+t3→j, 0≤t≤3r→(t)=t2i→+t3j→, 0≤t≤3

Find the directional derivative of the function
f(x,y)=x^6+y^3/(x+y+6 ) at the point (2,-2) in the direction of the
vector < - 2 ,2>.
b) Also find the maximum rate of change of f at the given
point and the unit vector of the direction in which the maximum
occurs.

Find and classify each critical point (as relative maximum,
relative minimum, or saddle point) of
f(x,y) = 2x^3 + 3x^2 + y^1 - 36x + 8y + 1

Consider the following function.
f (x, y) = (x −
6) ln(x5y)
(a)
Find the critical point of f.
If the critical point is (a, b) then enter
'a,b' (without the quotes) into the answer
box.
(b)
Using your critical point in (a), find the value of
D(a, b) from the Second Partials test
that is used to classify the critical point.
(c)
Use the Second Partials test to classify the critical point
from (a).
one of: relative max, relative...

In what direction does f(x,y)=ln(7x^2+8y^2) increase most
rapidly at (4,5)? Answer with a unit vector

part 1)
Find the partial derivatives of the function
f(x,y)=xsin(7x^6y):
fx(x,y)=
fy(x,y)=
part 2)
Find the partial derivatives of the function
f(x,y)=x^6y^6/x^2+y^2
fx(x,y)=
fy(x,y)=
part 3)
Find all first- and second-order partial derivatives of the
function f(x,y)=2x^2y^2−2x^2+5y
fx(x,y)=
fy(x,y)=
fxx(x,y)=
fxy(x,y)=
fyy(x,y)=
part 4)
Find all first- and second-order partial derivatives of the
function f(x,y)=9ye^(3x)
fx(x,y)=
fy(x,y)=
fxx(x,y)=
fxy(x,y)=
fyy(x,y)=
part 5)
For the function given below, find the numbers (x,y) such that
fx(x,y)=0 and fy(x,y)=0
f(x,y)=6x^2+23y^2+23xy+4x−2
Answer: x= and...

Find the urge of the function f over the given region. F(x,y) =
3x+7y over the triangle (0,0) (6,0) and (0,10)

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